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First Year Math Sets, Functions & Groups
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6. Supply the missing elements of the third row of the given table so that the operation ※ may be associative.\begin{tabular}{|c|c|c|c|c|}\hline ж & a & b & c & d \\\hline a & a & b & c & d \\\hline b & b & a & c & d \\\hline c & - & - & - & - \\\hline d & d & c & c & d \\\hline\end{tabular}
Example 1: Ordinary addition multiplication are operations on N . i.e. N is closed with respect to ordinary addition and multiplication because\[\forall a b \in N a+b \in N \wedge a . b \in N\]( \forall stands for" for all" and \wedge stands for" and")
Example 1: Ordinary addition multiplication are operations on N . i.e. N is closed with respect to ordinary addition and multiplication because\[\forall a b \in N a+b \in N \wedge a . b \in N\]( \forall stands for" for all" and \wedge stands for" and")
Example 4: If B=\{123\} then\[P(B)=\{\Phi\{1\}\{2\}\{3\}\{12\}\{13\}\{23\}\{123\}\}\]
Example 4: If B=\{123\} then\[P(B)=\{\Phi\{1\}\{2\}\{3\}\{12\}\{13\}\{23\}\{123\}\}\]

